{"files"=>["https://ndownloader.figshare.com/files/979612"], "description"=>"<p>Neural activities plotted as a time series of the overlaps with the target (), the input (), and a random pattern (). The random pattern is generated from the same ensemble of targets and inputs. <b>A.</b> The recall process before the learning for . <b>B.</b> The recall processes after the learning for (i) = (16,0.01) and (ii) = (1,0.5). The activity is spontaneous () or evoked () as indicated by the dotted and filled red bars, respectively, above the plots. The evoked activity is introduced by the application of an input of strength . In (ii), the time series from two initial conditions that lead to the two different attractors are plotted.</p>", "links"=>[], "tags"=>["processes"], "article_id"=>646272, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Recall_processes_before_and_after_the_learning_/646272", "title"=>"Recall processes before and after the learning.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:05:14"}

{"files"=>["https://ndownloader.figshare.com/files/979615"], "description"=>"<p><b>A.</b> The quenched average of the overlap with the target in the evoked dynamics. <b>B.</b> The standard deviation (SD) of the overlap averaged over time and over the networks . Average values in A and B are computed over 100 networks and over . The dotted curves in A and B, plotted for reference, show the boundary between the R and NR regimes and, which are computed by the ridge of SD in B with smoothing the line. <b>C.</b> The local maxima in the time series of the overlap with the target as a function of the input strength in (i) the NR regime for and (ii) the R regime showing the bifurcations.</p>", "links"=>[], "tags"=>["diagram", "evoked", "spontaneous", "bifurcation"], "article_id"=>646274, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Phase_diagram_of_the_evoked_and_spontaneous_dynamics_and_bifurcation_diagram_/646274", "title"=>"Phase diagram of the evoked and spontaneous dynamics and bifurcation diagram.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:05:41"}

{"files"=>["https://ndownloader.figshare.com/files/979623"], "description"=>"<p><b>A.</b> The overlaps with the target and input during the learning process (i) in the NR regime for and (ii) in the R regime for . <b>B.</b> The matrix elements , and in (i) the NR regime and (ii) the R regime with the same parameters as in A.</p>", "links"=>[], "tags"=>["overlap", "matrix"], "article_id"=>646276, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_time_evolution_of_the_overlap_and_the_matrix_elements_/646276", "title"=>"The time evolution of the overlap and the matrix elements.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:06:13"}

{"files"=>["https://ndownloader.figshare.com/files/979636"], "description"=>"<p>The time evolutions of ( = 1, 2, 3, 4, and 5) are indicated by different colors for . In the presence of each input (shown as the colored bar above the plot), the neural activity converges to the target to be learned. After convergence, a new mapping is provided, and in the presence of the new input, the system starts to learn the new target.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "physics", "mathematics"], "article_id"=>646281, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_learning_process_for_five_mappings_/646281", "title"=>"A learning process for five mappings.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:07:38"}

{"files"=>["https://ndownloader.figshare.com/files/979641"], "description"=>"<p><b>A.</b> The time series of the neural activities shown by the overlap with the 1st, 5th, and 30th targets in the absence and presence of the 1st (red), 5th (green), and 30th (blue) inputs (shown by the colored bars above the plot) for . <b>B.</b> The time-averaged overlaps with the learned targets as a function of (squares). The overlaps with the targets and inputs averaged over the 100 networks are shown as the solid and dashed lines, respectively. <b>C.</b> The distributions of the overlaps of the spontaneous activity with the targets. The black line represents the distribution averaged over 10 overlaps with 10 random patterns as a control, and the others are distributions of the overlaps , , and using the same colors as in A. <b>D.</b> The SD of the overlap with the target for the temporal evolution (squares), and the SD of the target and random pattern averaged over the 100 networks shown as the right blue and black lines, respectively.</p>", "links"=>[], "tags"=>["neural", "40", "steps"], "article_id"=>646284, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_neural_dynamics_after_40_learning_steps_in_the_response_R_regime_/646284", "title"=>"The neural dynamics after 40 learning steps in the response (R) regime.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:08:35"}

{"files"=>["https://ndownloader.figshare.com/files/979642"], "description"=>"<p><b>) = (16,0.01) in the R regime.</b> We use the network shaped after 40 learning steps. <b>A.</b> The local maxima in the time series of the overlap with the target in the presence of the corresponding input as a function of . The overlaps with (i) the 1st (), (ii) 5th (), and (iii) 30th () targets are plotted in red, green, and blue, respectively, while the data in black represent the overlap with each input (). <b>B.</b> The number of positive Lyapunov exponents of these evoked dynamics as a function of . Lyapunov exponents are calculated from the time series according to the algorithm in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002943#pcbi.1002943-vonBremen1\" target=\"_blank\">[56]</a>.</p>", "links"=>[], "tags"=>["diagram"], "article_id"=>646285, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.g008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bifurcation_diagram_for_/646285", "title"=>"Bifurcation diagram for (", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:08:56"}

{"files"=>["https://ndownloader.figshare.com/files/979644"], "description"=>"<p><b> and </b><b>. </b><b>A.</b> The capacity (as defined in the main text). The dotted line denotes the boundary of the R regime, computed by the line where the memory capacity goes beyond one, with smoothing the line. <b>B.</b> The average SD of the spontaneous activity. In A and B, we computed the capacity and SD by averaging over 100 network and . <b>C.</b> The temporal evolution of the overlap with the latest target in the absence () and presence () of the latest input with for in (i) and for in (ii), indicated by (i), and (ii), for in A and B. For (ii), results from two initial conditions that lead to differed attractors are plotted. <b>D.</b> The average of the overlap with the -th target in the presence of the -th input (magenta line) and the SD of the spontaneous overlap (right blue line) plotted as a function of for the parameter set indicated by (i) and (ii) in A and B. <b>E.</b> The exponents and , computed from a fit of the overlap and averaged SD to and , respectively. Both and are computed for different by fixing as represented by the magenta and right blue lines, respectively. <b>F.</b> The capacity for different by fixing .</p>", "links"=>[], "tags"=>["evoked", "spontaneous", "activities"], "article_id"=>646287, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.g009"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dependence_of_the_evoked_and_spontaneous_activities_on_/646287", "title"=>"Dependence of the evoked and spontaneous activities on", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-08 08:09:18"}

{"files"=>["https://ndownloader.figshare.com/files/979653", "https://ndownloader.figshare.com/files/979658", "https://ndownloader.figshare.com/files/979661"], "description"=>"<div><p>Recent experimental measurements have demonstrated that spontaneous neural activity in the absence of explicit external stimuli has remarkable spatiotemporal structure. This spontaneous activity has also been shown to play a key role in the response to external stimuli. To better understand this role, we proposed a viewpoint, “memories-as-bifurcations,” that differs from the traditional “memories-as-attractors” viewpoint. Memory recall from the memories-as-bifurcations viewpoint occurs when the spontaneous neural activity is changed to an appropriate output activity upon application of an input, known as a bifurcation in dynamical systems theory, wherein the input modifies the flow structure of the neural dynamics. Learning, then, is a process that helps create neural dynamical systems such that a target output pattern is generated as an attractor upon a given input. Based on this novel viewpoint, we introduce in this paper an associative memory model with a sequential learning process. Using a simple Hebbian-type learning, the model is able to memorize a large number of input/output mappings. The neural dynamics shaped through the learning exhibit different bifurcations to make the requested targets stable upon an increase in the input, and the neural activity in the absence of input shows chaotic dynamics with occasional approaches to the memorized target patterns. These results suggest that these dynamics facilitate the bifurcations to each target attractor upon application of the corresponding input, which thus increases the capacity for learning. This theoretical finding about the behavior of the spontaneous neural activity is consistent with recent experimental observations in which the neural activity without stimuli wanders among patterns evoked by previously applied signals. In addition, the neural networks shaped by learning properly reflect the correlations of input and target-output patterns in a similar manner to those designed in our previous study.</p> </div>", "links"=>[], "tags"=>["embedding", "responses", "spontaneous", "neural", "shaped", "sequential", "learning"], "article_id"=>646290, "categories"=>["Physics", "Mathematics", "Biological Sciences", "Neuroscience"], "users"=>["Tomoki Kurikawa", "Kunihiko Kaneko"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002943.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002943.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002943.s003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Embedding_Responses_in_Spontaneous_Neural_Activity_Shaped_through_Sequential_Learning__/646290", "title"=>"Embedding Responses in Spontaneous Neural Activity Shaped through Sequential Learning", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-03-08 08:10:36"}